Investor Carl Icahn has grabbed a stake valued at over $1.5 billion in Apple Inc.,AAPL-0.87% believing that more cash should be falling from the tech giant's branches.

Specifically, Mr. Icahn is pressing the company to buy back shares now.

While Apple earlier this year announced a large buyback, Mr. Icahn said in an interview Tuesday that he wants to see it happen right away, near the current share price, which he considers cheap.

"This is a no-brainer to go buy stock in a company that can go borrow" at a low rate, Mr. Icahn said in an interview. "Buy the company here and even without earnings growth, we think it ought to be worth $625," he said, referring to the stock price, which closed Tuesday at $489.57, having risen 5% on the news of Mr. Icahn's investment.

Mr. Icahn's thesis rests on Apple borrowing at about a 3% interest rate and buying back shares right now, likely at around $525 a piece. A stock buyback can increase earnings per share by reducing the number of shares outstanding.

Using Twitter on Tuesday to publicize his move, Mr. Icahn—who is known for buying large positions in various companies and then agitating for change—said he had a "nice" conversation with Tim Cook, Apple's chief executive, and discussed his opinion that "a larger share buyback should be done now." He added that he plans to speak with Mr. Cook again "shortly."

The tweets didn't disclose the size of the stake but a person familiar with the position said Mr. Icahn's stake is worth more than $1.5 billion.

Wielding influence at Apple won't be easy, or inexpensive, given a stock market value that currently stands at close to $450 billion. At that capitalization, Mr. Icahn's stake would be less than 1%.

Steve Dowling, an Apple spokesman, said the company appreciates the interest and investment of all its shareholders. "Tim had a very positive conversation with Mr. Icahn today," he said, without elaborating.

The investment is the second time in recent months an activist investor has targeted Apple, adding to the pressures on a company whose shares have dropped sharply since reaching all-time highs above $700 a share in September.

Earlier this year, David Einhorn, founder of Greenlight Capital Inc.,GLRE-0.93% pushed Apple to return more money to shareholders through a preferred stock plan. In a series of statements, Mr. Einhorn criticized Apple for being stingy with its large and growing cash reserves.

Apple said it believed it was taking the most prudent course, and in April increased its buyback authorization to $60 billion from the $10 billion announced last year. The company said the move marks the largest single share repurchase authorization of any company in history and it is expected to finish by the end of calendar 2015. In July, Apple said it had already spent $16 billion to repurchase shares in its third quarter ended in June.

Mr. Icahn's use of his Twitter account for the news was an unusual movie in itself, marking one of the first times such a position has been initially disclosed through the medium.

Mr. Icahn has lately been engaged in a battle over the future of Dell Inc., whose CEO and founder is trying to take the company private. Mr. Icahn holds a stake of nearly 9% in the computer maker.

In the interview Tuesday, Mr. Icahn, who plays chess on his iPad, said he made the Apple investment on the advice of his son Brett Icahn and investment partner David Schechter, who have been looking at the technology sector for Icahn EnterprisesIEP-0.89% LP.

Those two also led Mr. Icahn's successful investment in video provider Netflix Inc.NFLX2.47% where they have made $1 billion in less than a year. They pitched Mr. Icahn on Apple's solid cash position and its ability to borrow with ease to fund a massive stock buyback, Mr. Icahn said.

They also are bullish on Apple's ability to increase earnings, and expressed enthusiasm over the possibility that Apple's coming products, such as the widely anticipated watch and television, will drive sales.

Analysts have expressed concerns about a slowing pace of innovation at Apple, arguing that it hasn't launched a brand new product line since it released the first iPad in 2010. Other missteps for the Cupertino, Calif., trendsetter include a widely panned new mapping service for its iPhones and iPads.

On the financial front, the company has been under heavy scrutiny by various investors complaining about the size of its cash stockpile, which was recently reported as $146.6 billion. In March last year, Apple agreed, saying it had more cash than it needed to run its business, and began a dividend and share buyback program.

Mr. Icahn's move into Apple is the latest example of activist investors pursuing big game, in this case the largest company in the Standard & Poor's 500-stock index. For executives and boards of companies large and small, anticipating, managing and responding to activist shareholders has emerged as a significant and ongoing task, not to mention a source of revenue for advisers on Wall Street who help companies with the challenge.

What is unclear is what comes next. Mr. Icahn's typical investment methods are to buy a large chunk of a company stock and agitate for changes to the company's management, how they use cash or other strategies he believes will boost stock prices.

Mr. Icahn also is known for picking fights with executives and directors of companies he believes aren't acting in the interests of shareholders, including management at technology companies such as Netflix and Yahoo Inc. So far, both Mr. Icahn and Apple said the talks were amicable.

In his battle involving Dell, Mr. Icahn argues that CEO Michael Dell's plan for a buyout amounts to theft from shareholders.

In his bid to derail the proposed $24.8 billion deal, Mr. Icahn has said repeatedly in interviews that he wants to fire Mr. Dell as CEO. He added in a public letter that Mr. Dell has been "whining" about the terms of the buyout deal.

Last month, the Dell special committee reviewing the transaction said it had "reservations" about Mr. Icahn's methods of valuing Dell's stock, and directors have criticized him for abandoning repeated proposed deals involving the company.

Gene Munster, an analyst at Piper Jaffray, said Mr. Icahn's investment serves as an acknowledgment that better things could be coming from Apple over the next six months, which should help raise the company's stock. But he doesn't expect Mr. Icahn's influence to have much impact beyond the way Apple allocates its capital.

Share buybacks have enjoyed newfound popularity in the last couple of years, after companies that hoarded cash in the wake of the financial crisis have looked for ways to put it to work.

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